A clamping assembly with a clamping cone axially movable via a tension rod and several claw-like clamping elements spaced from each other on its outside in the peripheral direction is known from DE 101 59 611 C1. The claw-like clamping elements have oblique first clamping surfaces on their front end to contact corresponding oblique clamping slopes of the hollow shank tool, and second oblique clamping surfaces on their rear end for contact on a corresponding mating surface of the machine spindle. The clamping cone, designed as a single piece, has first conical clamping surface areas on its front end and second conical clamping surface areas on its rear end for contact on corresponding inside surfaces on the front and rear ends of the claw-like clamping elements. By axial displacement of the clamping cone arranged on the end of a tension rod, the claw-like clamping elements are pushed radially outward or inward in a position parallel to the center axis of the machine spindle so that the hollow shank tool can be clamped or released.